Are we talking theoretically, or are we talking practically? Because practically there are many choices out there for a cheap laptop that is capable of running arbitrary code.
Cheap : yes.
But cheap isn't the only characteristic that attract people to chromebooks.
The form factor is also another reason.
And most of the "run arbitrary code, and easily install Linux on them" devices tend to be heavy clunky workstation-class laptops
(again for obious market reasons : most linux users tend to be developers, its best to concentrate effort to create pro-laptops catering to them)
Chrome books tend to be extremely light and thin.
If you're on the market of a machine which doesn't break your back, and for which you hope to get supported drivers you best bets are in order : ChromeBooks then Windows ultraportable.
Usually, forget about MacBook Air, their weird embed controller won't get driver support quickly.
And that's for ulta-thin portable.
Then there are smartphone.
There it's very hard to find device allowing end-users to install arbitrary code. Usually you'll find it only on special hobbyist-oriented platforms, which tend to be expensive and with lower hardware specs (due to smaller production runs) like OpenMoko/GoldeDelicious FreeRunner/GTA04, like Pyra handheld console, etc.
There are a few consumer-oriented platforms that can optionally allow you to run arbitrary code : the above mentionned Jolla 1 by the former sacked R&D team of Nokia, Palm / HP's Pre (and the tendency has now halted, after switching hands to LG), etc.
And in between (still a smaller production run and a bit expensive for not-stellar specs. But more consumer-oriented than hobbyist oriented) : Fairphone 2.